Find the solution of the given Initial Value Problem by using the Laplace Transform Method. y'''-2y"+5y'=t , y(0)=0 , y'(0)=1 , y"(0)=2

geduiwelh

geduiwelh

Answered question

2021-09-12

Find the solution of the given Initial Value Problem by using the Laplace Transform Method.
y2y+5y'=t , y(0)=0 , y'(0)=1 , y(0)=2

Answer & Explanation

Demi-Leigh Barrera

Demi-Leigh Barrera

Skilled2021-09-13Added 97 answers

Solution:
y2y+5y'=t , y(0)=0 , y'(0)=1 , y(0)=2
L{y}=s3L{y}s2y(0)sy(0)y"(0)
L{y"}=s2L{y}sy(0)y(0)
L{y}=sL{y}y(0)
Step 2
Apply Laplace transform we get
[s3L{y}52]2[s2L{y}1]+5[sL{y}]=L{t}
(s32s2+5s)L{y}s=1s2
(s32s2+5s)L{y}=1s2+s
L{y}=1s3(s22s+5)+1(s22s+5)
L{y}=11251s+2251s2+151s3+s1251(s22s+5)121251(s22s+5)+1(s22s+5)
L{y}=11251s+2251s2+151s3+s1251(s22s+5)+1131251(s22s+5)
Apply Inverse Laplace transform
y=1125+225t+t210+et125[sin(2t)2+cos(2t)]+113125[etsin(2t)2]
y=1125+2t25+t210+etcos(2t)125+114etsin(2t)250
This is required solution

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